Goal
Convert 135 lbs to kilograms using dimensional analysis (unit cancellation). In classical mechanics, “lb” can mean pounds-force (force) or pound-mass (mass); in a standard lbs to kg conversion, lb is interpreted as pound-mass.
Step 1: Use the exact conversion factor
The pound-mass is defined in terms of the kilogram by: \[ 1\ \text{lb} = 0.45359237\ \text{kg} \]
Step 2: Set up dimensional analysis (units cancel)
Multiply by a ratio equal to 1, arranged to cancel lb: \[ 135\ \text{lb} \times \frac{0.45359237\ \text{kg}}{1\ \text{lb}} \]
The lb unit cancels, leaving kilograms.
Step 3: Perform the calculation
\[ 135 \times 0.45359237 = 61.23496995 \] \[ 135\ \text{lb} = 61.23496995\ \text{kg} \]
Step 4: Round using significant figures
The value 135 has three significant figures. The conversion factor is exact, so the result is reported to three significant figures: \[ 61.23496995\ \text{kg} \approx 61.2\ \text{kg} \]
Final result: 135 lbs to kg gives \(61.2\ \text{kg}\) (3 significant figures).
Quick check (sanity check)
Since \(1\ \text{kg} \approx 2.20462\ \text{lb}\), converting back should return about 135 lb: \[ 61.23496995\ \text{kg} \times 2.20462\ \frac{\text{lb}}{\text{kg}} \approx 135\ \text{lb} \]
Visualization: one-step conversion with unit cancellation
Optional mechanics note: weight as a force
If a mass \(m = 61.23496995\ \text{kg}\) is needed to estimate weight near Earth using \(W = m g\) and \(g = 9.80665\ \text{m/s}^2\), then: \[ W = 61.23496995 \times 9.80665 \approx 600.5095953\ \text{N} \]